Interpretting the Eigen and Betweenness centrality

[asohfrank]

I have a network that, when i run both the eigenvector and betweenness centrality measures, i have nodes of higher influences thus :

Among the top 10 nodes in betweenness centrality ranking results, about 5 of them appear in the top 10 of eigenvector results and the rest dont.

I do not fully understand why each centrality measure has it's own leaders but then again that's why there are many different centrality measures.

Can someone please explain to me situations where a node will be a betweenness leader and not be an eigenvector leader ?

[kc2519]

Sorry for late response - betweenness centrality tells you which nodes are most critical for connecting other nodes to one another. If this score is high, then many paths must travel through a certain node to connect to others. Eigdenvector is more concerned with the influence of the nodes a specific node is connected to. If many of these neighbor nodes are considered important (high degrees of their own) then the eigenvector score will be high.

[Skedasticity]

If it's still of interest, consider the following - eigenvector centrality is essentially degree (number of direct connections) that a node has weighted by the degrees of her connections. In my experience the correlation between various centrality measures can be surprisingly low, say, 35%. Betweenness and eigenvector simply measure different things, and thus while there will be overlap in leadership, you can have a large network (degree/eigenvector) but still be on the periphery of a larger community and/or have few connections but be in the "center" of the information flows (betweenness).